Sunday, May 12, 2013

Magical Math Sticks and Cover Case

This one is for my father, who still uses a slide rule.

William Oughtred, an English mathematician, invented the slide rule using Napier’s theory.
In 1614, John Napier, a Scottish mathematician, invented logarithms to simplified complicated multiplication and division calculations.  
He used wooden sticks (called Napier's Bones or Rods) to show the multiplication tables 1 through 9.
These Magical Math Sticks are a crocheted version of Napier’s Bones.

This pattern is fairly easy.
The paired-stitches create a clear hole to embroider the numbers on both sides.
And there is a colorful edging around the sticks.
There are 11 Bones (each with 2 sides), so the project can be a bit time consuming.
But sometimes repetition can be soothing.
And in the end, I think it is worth it.

There are many web sites about Napier’s Theory that can be explored.
Here is a quick explanation of the Bones:
Note: There is a reason that I did not become a teacher so bear with me.

There is a Guide Stick with Numbers 1 through 9.
On the other sticks, a slanted line separates the tens digit on the left from the units digit on the right.
To multiply:
Place the Guide Stick to the left,
and the number stick you want to multiply, to the right of it.  

Example: 6 x 7:
If you read across from the number on the Guide Stick (which is #6), you see that the #7 stick has a 4 in the ten’s place and a 2 in the one’s place. (6 x 7 Answer: 42).

Use the bones to multiply 9 x 82:
Place the #8 and #2 sticks to the right of the Guide Stick.
Read across from the Guide number (which is #9).
[Numbers that are contained in the parallel diagonals are added together.  Here the 2 and the 1 are in the ten’s place.]
 The answer will read across: [7 hundred’s] [2 + 1 = 3 Ten’s] [8 One’s]   So the answer is 738.

The Bones can be used to do much more complicated multiplication and division.
And there are many web sited that can explain it much better than I can.
Like I said….. “Not a teacher.”

~ = Approximately
Beg = Beginning
Ch(s) = Chain(s)
Dec = 2 stitches worked together
FO = Fasten Off
Lp(s) = Loop(s)
Sc = Single Crochet
Ss = Slip Stitch
St(s) = Stitch(es)

US Terminology

* Crochet Thread: size #10 (at least 2 different colors)
Main Base Color: ~360 yds. of Cream (or any light color)
                       Note: ~16 yds. for each panel side (22 sides needed)
Numbers:  ~44 yds. of Black (or a dark color)
Note: ~2 yds. for each panel side
(If you wish, Edging and Embroidered Numbers can all be done in the same color.
And instead of Crochet thread #10, you could use DMC Floss.)
Edging: ~55 yds.
            Note: ~5 yds. for each stick
Can be all the same color or 11 different shades.
For one set, I used Lt Blue, Pink, Purple, Turquoise, Yellow, Green, Red, Brown,
            Orange, Dk Blue (and Variegated for the Main Stick)
* 1.50 mm steel hook (~ US size 8)
* A Small Embroidery Needle for the Crochet Thread (used for numbers and weaving in ends)
* Plastic Canvas (7 holes to the inch): Cut to the dimensions of the panel-side.
I used 42 holes long and 4 holes wide for each panel for (~ 6.5” x .5”)
The plastic canvas size could be different, if you crochet tighter or looser, or if you use a different size hook or thread.
When you complete Rows 1–57, be sure to measure, before you cut the canvas.
What do they say? “Measure twice, cut once”.  Better to be a bit big, than too short.
You will need to cut 11 plastic canvas sticks.
Gauge9 sc and 9 Rnds = ~1”   Not crucial.

Finished Size: ~ 6 ½” Long and 1” Wide (16.5cm x 2.5cm)

Pattern Notes:
I used crochet thread because it rendered a nice size stick to hold in your hands.
If you wanted larger sticks, I suppose you could use just about any type of yarn or hook.

I used a plastic canvas sheet because it was relatively strong and flexible.
However, you could use cut plastic, such as Costco packaging.
Just measure the panel size before cutting the plastic insert.
Round the edges slightly, so it will not be sharp at the corners.
And make sure it is smooth on the sides, to easily slip in between the panels.

Use a light color for the panels so the numbers will stand out.
If you prefer, you can make the Guide Stick panel in a different (light) color.
I used cream color for 10 sticks (20 panels) and a yellow or for the Guide (2 panels).

The paired single-crochet stitch creates a clear hole to embroider the numbers.
If you wish, you can simply crochet 57 rows of plain single crochets.
I did try that, but embroidering the numbers was a bit more difficult and took longer.
Regarding copyright:
This is a free pattern for your personal use.
You are welcome to sell any items that you make.
But please, do not sell the pattern or reproduce the text without permission.

Panel: (Note: 22 panels are needed for 11 sticks)
Row 1:  Ch 8, Sc in the back ridge-bump of 2nd ch from the hook, and each ch across.  Turn.  (7)
Row 2:  Ch 1. 
First Paired Stitch:
Insert hook into first st, YO, pull up a loop (2 lps on the hook now)
Insert hook in next st, YO and pull up a loop (now there should be 3 lps on the hook).
YO and pull thru all 3 loops.
Note: The paired SC stitch is basically a Sc decrease.
Next Paired Sts:
            * Sc-Dec by pulling up a loop from the same as the last st and the next st.*
Repeat from * to * 4 more times.
Sc in the same as the last st (to keep an even count).   Turn.  (6 paired + 1 sc = 7 sts)
Rows 3 - 56:  Repeat Row 2. 
Row 57:  Ch 1, Sc across.  FO.  (7)

Embroider Numbers: 
The Guide Stick can have the numbers 1 - 9 embroidered on just the front side.
 Or both sides, if you prefer.
The Main Sticks have counterpart Front and Back sides.
Two sticks will have a “0” on one side with a “9” on the opposite side.
Similarly, there will be two sticks for the 1 and 8, 2 and 7, 3 and 6, and the 4 and 5.

You will note that there are 9 horizontal lines and 8 diagonal lines across each of the main 10 sticks.
The Guide Stick just has 9 horizontal lines.
There are 7 single crochets across the crocheted panels.
The chain-1-turns produce an added segment that counts as the eighth square in the graph.
Follow the graph-chart, and backstitch the black numbers and lines on each panel.
The red lines just show the outer-edge dimensions of each panel.
You will need to make two of each number-panel. 
Weave in ends when finished.
Side Note:  If you want, you can slant the diagonal lines in the opposite direction (to the left).
But be sure to make all 20 diagonal-panels in a set consistently the same.

 Edging Notes:  The Guide Stick should have an edging that stands out: like Black or Variegated.

Start by Matching the embroidered-number panels:
You can make the two matching sticks the same color (to identify them easier).
Possible colors:
0 and 9 = Red
1 and 8 = Blue
2 and 7 = Yellow
3 and 6 = Green
4 and 5 = Orange

Hold two corresponding panels (i.e. 0 and 9) with wrong sides together.  The numbers sides should be facing out on both.
Stitch the 0 as the right side (with the 9 as the back side) of one stick.
And the 9 as the right side (with the 0 as the back side) of the second stick.
Continue with the rest of the sticks, so each of the 10 numbers will have a right side.
If you prefer, you can use a reverse-sc stitch for the edgings.

Periodically keep track of back side to make sure that you have not missed a stitch or gone off track.
The horizontal lines should meet on both front and back sides.
There should be 5 stitches between each horizontal line.
Be especially careful on the row back up the 2nd long side.  The back part tends to shift up a bit.
Also note, you will be single crocheting completely over the 7 stitches of the first and last rows (the short ends).  This produces a thicker top and bottom to compensate for the added plastic insert.

Edging:  Now….Keeping the two aligned:
3 Sc through both layers, in the right-corner-stitch on the bottom.
Sc up the panel (54 sts) and 3 Sc in the next corner st.
Sc across the top next 5 sts with 3 Sc in the next corner.
Continue to Sc down the other side about 20 to 30 sts.
Then insert the plastic canvas between the two panels.
Continue to Sc to the bottom with 3 Sc in the final corner.
Sc across the bottom last 5 stitches. Join to the first sc with a ss. 
FO and weave in.

 © 2013 P Perkins


Holding Case:

Caron Simply Soft (WW Med yarn):
Can be made in Various colors   
I used: ~ 60 yds of Red for the cover
~ 55” of Black for the letters
E / 3.5 mm
Rounded yarn needle to sew letters

Gauge:  9 sc and 10 Rnds = ~ 2”  Not crucial.
            Round 2 should = ~ 3 ½” x 1 ¼”
Note: Adjust hook size, for a larger or smaller one.

Finished Size:          Height ~6”
Width ~3”
                        Depth ~1 ¼”

~ = Approximately
BLO = Back Loop Only
Ch(s)= Chain(s)
FO = Fasten Off
Hdc = Half Double Crochet

Rnd(s) = Round(s)

Sc = Single Crochet
Sc-Inc = 2 single crochets in one stitch
Ss = Slip Stitch
St(s) – Stitch(es)

US Terminology
Regarding copyright:
This is a free pattern for your personal use.
You are welcome to sell any items that you make.
But please, do not sell the pattern or reproduce the text without permission.

Rnd 1: Ch 15.
3 Hdc in 3rd ch, [Mark first hdc]
Hdc in next 11, 5 Hdc in last ch.
Working other side of ch:
Hdc in next 11, 2 Hdc in same as first-3-hdc’s.
Join to first (marked) st with a ss.  (32)
Rnd 2: Ch 1,
Sc in same as the joined st and the next st,
            Sc-Inc in next, Sc in next 11 sts,
            Sc-Inc in next, Sc in next 3, Sc-Inc in next,
Sc in 11, Sc-Inc, Sc in last st and join to the first st.  (36)
          Now work in a spiral. 
          Do not join or ch 1. 
          Mark beg of rnds.
Rnd 3: Sc in BLO of each st around.  (36)
After Rnd 6, check to make sure that the bones will fit.
Rnds 4 30: Sc in the 1st st and around.  (36)
            At the end of rnd 30, ss in the next 2 sts, FO and weave in.

Put the bones in the case and mark where the front edges are, so lettering will be even on front.
Then, remove the bones and start about 6 rows down from the top edge, and very close to the left side (marked) edge with the capital “N”.  I used about 54” of Black yarn for the Letters.
I made the “N” over 3 rows and the “APIER’S” over 2 rows.
The “B” should begin 2 rows down and start under the “A”.
Note:  You could leave the case blank, or add a name, if you prefer.
2013 P Perkins